A prosthetic aortic valve includes an annular, annulus inflow portion that is designed to reside in or near the patient's native aortic valve annulus, and an annular, aortic outflow portion that is designed to reside in the patient's aorta downstream from at least a portion of the valsalva sinus. The annulus inflow portion and the aortic outflow portion are connected to one another by a plurality of connecting struts that are confined to regions near the commissures of the patient's native aortic valve. The connecting struts are designed to bulge out into the valsalva sinus to help anchor the prosthetic valve in place. The valve is circumferentially collapsible to a relatively small diameter for less-invasive delivery into the patient. The valve circumferentially expands to a larger operational diameter when deployed at the implant site.